Many thanks to all those who posted or sent Cusco and me their suggestions on places to fly. We went to LA, and picked up an Arrow from ADP. The hourly rate was excellent (we paid upfront for a 40-hour block).
We didn't take the advice to fly to Florida and back, but we did fly well over 3,000nm across California, Arizona, and Nevada. Many thanks for the excellent suggestions from many PPRuNers - we took up as many as we could fit in.
The weather was kind to us, too - it was IMC the first day, which made the BFR and IPC easier. We then filed IFR from Brackett to Santa Barbara (which was VFR but very windy when we got close), and IFR back after lunch - through some seriously turbulent clag. That prepared us reasonably for all that was to come.
After that it was scorchingly hot (hottest days for N years were reported several times as we flew around - maybe we were towing the hot weather behind us!). We used Big Bear (6,748amsl) as our cooling-off resort.
The whole route was
Brackett - Palm Springs - Chino - Brackett - Big Bear - Brackett (BFR and IPC for two of us). Then Brackett - Santa Barbara - Brackett for some IFR practice. That was day 1.
Then Brackett - North Las Vegas - Grand Canyon - Page - North Las Vegas - Furnace Creek (Death Valley) - California City - San Luis Obispo - Monterey - San Francisco and the Bay Tour, Golden Gate Bridge Overflight, Alcatraz (from a safe distance) - Napa County. There we had a day off flying to sample the scenery and the wine (well, it was Cusco's birthday).
Then from Napa County to Van Nuys - the busiest GA airport in the world, they told us. It was certainly busy when we were there, but we got the same courteous and helpful handling as the Citations and Lears etc that were arriving and departing.
From Van Nuys we went to the Flyer List fly-in at Chiriaco Summit, then Big Bear - Lake Havasu City - Palm Springs - Big Bear - Agua Dulce - Santa Barbara - Chino (for the Planes of Fame Museum) - Brackett. Then by BA from LAX to Heathrow.
Places we'd recommend: all of them, maybe with the exception of Las Vegas. The airport was fine, but the town...
Scary experiences:
crossing the Grand Canyon via the corridor - stunning views but not many places to go if the engine quits;
flying towards Tehachapi from Death Valley with the ASI indicating 130 knots and the DME showing 45 - not that it was windy
some stonking crosswinds at some desert airstrips (fortunately none above the Arrow's or our limits).
Good experiences: too many to mention! The FBOs everywhere were extremely courteous and helpful to two scruffy Brits in a dirty old Arrer, despite all the glossy bizjets and smart folks with collars and ties and epaulettes that were coming at them from other directions. And the scenery - well! There's nothing like it anywhere round here.
Flying in mountains seems not to be the big deal it is in Europe. The safety rules need to be followed (2000 feet above, work out where the up and downdrafts are, cross at 45 degrees), but there isn't the sharp intake of breath through teeth when you mention it. We had no frights whatever - but then, we had flight following on radar wherever we went.
Places to visit again: most of them!